What is 4+2ln((sqrt(2)+1)/(sqrt(2)-1)) ?

The solution to 4+2ln((sqrt(2)+1)/(sqrt(2)-1)) is 4+2(ln(sqrt(2)+1)-ln(sqrt(2)-1))

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simplify 4+2ln((sqrt(2)+1)/(sqrt(2)-1))

simplify

4 + 2 ln (\frac{2 + 1}{2 - 1})

4 + 2 (ln (2 + 1) - ln (2 - 1))

Decimal Notation

7.52549 \dots

Solution steps

4 + 2 ln (\frac{2 + 1}{2 - 1})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{2 + 1}{2 - 1}) = ln (2 + 1) - ln (2 - 1)

= 4 + 2 (ln (1 + 2) - ln (2 - 1))

d + θ ln (k) + γ ln (ω) - ln (\frac{1}{1 + βθ} k^{α} ω) - β d

6 lo g_{8} (u) + 6 lo g_{8} (w) - 36 lo g_{8} (v)

- lo g_{10} (5 \cdot 1 0^{8})

ln \frac{( x ( x ^{2} + 1 ) ^{2} )}{2 x ^{3} - 1}

4 \cdot ln (- 1) + ln (4)

What is 4+2ln((sqrt(2)+1)/(sqrt(2)-1)) ?
The solution to 4+2ln((sqrt(2)+1)/(sqrt(2)-1)) is 4+2(ln(sqrt(2)+1)-ln(sqrt(2)-1))